A280520 Triangle read by rows: T(n,k) = number of increasing sequences of n positive integers with reciprocals adding up to k (k=1,2,...,A055980(n)).

1, 0, 1, 6, 1, 72, 6, 2320, 72, 245765, 2320, 151182379, 245765

Offset: 1

Author

Max Alekseyev, Jan 04 2017

Keywords

• nonn
• tabf
• more

Comments

T(n,k) = 0 for all k > A055980(n).

For n=3,...,11, we have T(n,2) = T(n-1,1). However, T(12,2) > T(11,1).

Conjecture: for n in A115515 (i.e., A055980(n+1)=A055980(n)+1), the sequences being enumerated by T(n,A055980(n)) must start with 1. E.g., there is no 10-tuple (x_1,x_2,...,x_10) with 1 < x_1 < ... < x_10 and 1/x_1 + ... + 1/x_10 = 2 (=A055980(10)).

Examples

			Triangle starts with:
n=1: 1
n=2: 0
n=3: 1
n=4: 6, 1
n=5: 72, 6
n=6: 2320, 72
n=7: 245765, 2320
n=8: 151182379, 245765
...
		

Crossrefs

Cf. A280518 (row sums), A006585 (column k=1), A156869 (nondecreasing sequences), A280519 (ordered sequences).